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Proof step 3 from proof uni (previous step)

rs0 ∩ rs1 = ∅ ⊦ mk(rs0 ∪ rs1, f) = mk(rs0, f) ∪ mk(rs1, f)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r]))
Proof step 5:
rs0 ∩ rs1 = ∅ ⊦ ∀ r. (r ∈ mk(rs0 ∪ rs1, f) ↔ r ∈ mk(rs0, f) ∪ mk(rs1, f)) ∧ (r ∈ mk(rs0 ∪ rs1, f) → mk(rs0 ∪ rs1, f)[r] = (mk(rs0, f) ∪ mk(rs1, f))[r])

Rule argument

spec: heap name: ext seq: ⊦ H0 = H1 ↔ (∀ r. (r ∈ H0 ↔ r ∈ H1) ∧ (r ∈ H0 → H0[r] = H1[r])) subst: [H1, H0] → [mk(rs0, f) ∪ mk(rs1, f), mk(rs0 ∪ rs1, f)] flags: <all paths>

Additional information

Used terms: mk(rs0, f) ∪ mk(rs1, f), mk(rs0 ∪ rs1, f)